Passive learning and input-to-state stability of switched Hopfield neural networks with time-delay

Exponential input-to-state stability of recurrent neural networks with multiple time-varying delays

“…Recently, some results on ISS or IOSS were obtained in (Sanchez and Perez 1999;Ahn 2010bAhn , 2011aAhn , b, 2010c. However, these results were restricted to non-delay or constant delay.…”

“…However, these results were restricted to non-delay or constant delay. In contrast to the results (Sanchez and Perez 1999;Ahn 2010bAhn , 2011aAhn , b, 2010c, we consider dynamical neural networks with multiple time-varying delays which may be more accurate to describe the evolutionary process in some real systems. Furthermore, we firstly investigates the exp-ISS of the RNNs, which attains a much faster convergence rate.…”

“…Due to its wide applications in various areas such as pattern classification, associative memory, parallel computation, optimization, moving object speed detection and so on, recurrent neural networks (RNNs) have been extensively studied by researchers in recent years (see, e.g., (Hopfield 1984;Hopfield and Tank 1986;Grujiá and Michel 1991;Matsouka 1992;Arik 2000;Ensari and Arik 2005;Zhang et al 2008;Wu et al 2008Wu et al , 2010Huang et al 2012;Huang and Feng 2009;Ahn 2010a;Liu and Cao 2010;Ahn 2010bAhn , c, 2011aAhn , b, 2012aSanchez and Perez 1999;Zhu and Shen 2012) and references therein). Since time-delay is unavoidably encountered in implementation of RNNs and is frequently a source of oscillation and instability, the stability of delayed neural networks has become a topic of great theoretical and practical importance, and many interesting results on stability in the Lyapunov sense have been derived (see also e.g.…”

“…control in Feng 2009 andAhn 2010a and state estimation in Cao 2010and Ahn 2012a), were given to discuss the influence of disturbances for the dynamical behaviors of the networks. Some dynamical properties such as robustness (see, e.g., Wu et al 2010;Huang et al 2012;Ahn 2012b), passivity (see Ahn 2011bAhn , 2012c, input-to-state stability (see Sanchez and Perez 1999;Ahn 2010bAhn , 2011aAhn , b, 2010cZhu and Shen 2012) also are investigated for the networks with disturbances. Among these properties, the input-to-state stability (ISS) are widely accepted as an important tool to check robust stability since the ISS properties imply not only that the unperturbed system is asymptotically stable in the Lyapunov sense but also that its behavior remains bounded when its inputs are bounded.…”

“…For example, Sanchez and Perez (1999) firstly investigated the ISS properties and gave some matrix norm conditions on ISS for RNNs. Ahn (2010b) proposed passivity-based learning law to investigate the ISS for a class of switched Hopfield neural networks with time delay. Also in Ahn (2011a), by employing a suitable Lyapunov function, a new sufficient condition is derived to guarantee ISS of Takagi-Sugeno fuzzy Hopfield neural networks with timedelay.…”